How to move a camera using in a ray-tracer?

Question

I am currently working on ray-tracing techniques and I think I've made a pretty good job; but, I haven't covered camera yet.

Until now, I used a plane fragment for view plane which is located between (-width/2, height/2, 200) and (width/2, -height/2, 200) [200 is just a fixed number of z, can be changed].

Addition to that, I use the camera mostly on e(0, 0, 1000), and I use a perspective projection.

I send rays from point e to pixels, and print it to image's corresponding pixel after calculating the pixel color.

Here is a image I created. Hopefully you can guess where eye and view plane are by looking at the image.

My question starts from here. It's time to move my camera around, but I don't know how to map 2D view plane coordinates to the canonical coordinates. Is there a transformation matrix for that?

The method I think requires to know the 3D coordinates of pixels on view plane. I am not sure it's the right method to use. So, what do you suggest?

Answer 1

There are a variety of ways to do it. Here's what I do:

1. Choose a point to represent the camera location (camera_position).
2. Choose a vector that indicates the direction the camera is looking (camera_direction). (If you know a point the camera is looking at, you can compute this direction vector by subtracting camera_position from that point.) You probably want to normalize (camera_direction), in which case it's also the normal vector of the image plane.
3. Choose another normalized vector that's (approximately) "up" from the camera's point of view (camera_up).
4. camera_right = Cross(camera_direction, camera_up)
5. camera_up = Cross(camera_right, camera_direction) (This corrects for any slop in the choice of "up".)

Visualize the "center" of the image plane at camera_position + camera_direction. The up and right vectors lie in the image plane.

You can choose a rectangular section of the image plane to correspond to your screen. The ratio of the width or height of this rectangular section to the length of camera_direction determines the field of view. To zoom in you can increase camera_direction or decrease the width and height. Do the opposite to zoom out.

So given a pixel position (i, j), you want the (x, y, z) of that pixel on the image plane. From that you can subtract camera_position to get a ray vector (which then needs to be normalized).

Ray ComputeCameraRay(int i, int j) {
  const float width = 512.0;  // pixels across
  const float height = 512.0;  // pixels high
  double normalized_i = (i / width) - 0.5;
  double normalized_j = (j / height) - 0.5;
  Vector3 image_point = normalized_i * camera_right +
                        normalized_j * camera_up +
                        camera_position + camera_direction;
  Vector3 ray_direction = image_point - camera_position;
  return Ray(camera_position, ray_direction);
}

This is meant to be illustrative, so it is not optimized.